Lotteries and expected utility The preference of lotteries Continuous:L,L,L"∈ a∈[0,1:aL+(1-a)L%L"}c[0,1 a∈[0,1:L"%aL+(1-a)L}c[0,1 Independence axiom aL+(1-a)"%aL+(1-a)L"<→L%LLotteries and expected utility • The preference of lotteries: – Continuous: – Independence axiom: L L L , ,  L { [0,1]: (1 ) } [0,1]     + −  L L L   % { [0,1]: (1 ) } [0,1]     + −  L L L   %     L L L L L L + − + −  (1 ) (1 )     % %